(B) The velocity of a transverse wave in a stretched string is given by $v = \sqrt{\frac{T}{\mu}}$,where $T$ is the tension and $\mu$ is the linear ma

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(B) The velocity of a transverse wave in a stretched string is given by $v = \sqrt{\frac{T}{\mu}}$,where $T$ is the tension and $\mu$ is the linear mass density.Linear mass density $\mu = \rho A = \rho (\pi R^2)$,where $\rho$ is the density of the material and $R$ is the radius of the cross section.Since both strings are made of the same material,$\rho$ is constant. Given that the tension $T$ is the same for both strings,we have $v \propto \frac{1}{\sqrt{R^2}} \propto \frac{1}{R}$.Therefore,$\frac{v_2}{v_1} = \frac{R_1}{R_2}$.Given $R_1 = R$ and $R_2 = R/2$,we get $\frac{v_2}{v_1} = \frac{R}{R/2} = 2$.

Class 11 Physics Waves and Sound Speed of Mechanical Wave on String (Transverse wave)

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Two strings with circular cross section and made of same material are stretched to have the same amount of tension. $A$ transverse wave is then made to pass through both the strings. The velocity of the wave in the first string having the radius of cross section $R$ is $v_1$,and that in the other string having radius of cross section $R/2$ is $v_2$. Then $\frac{v_2}{v_1} = $

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$\sqrt{2}$
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$2$
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$8$
D
$4$

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Speed of Mechanical Wave on String (Transverse wave)

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$A$ transverse wave is passing through a string as shown in the figure. The mass density of the string is $1 \ kg/m^3$ and the cross-sectional area of the string is $0.01 \ m^2$. The equation of the wave in the string is $y = 2 \sin(20t - 10x)$. The hanging mass is (in $kg$):-

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$A$ rope of length $L$ and mass $M$ hangs freely from the ceiling. If the time taken by a transverse wave to travel from the bottom to the top of the rope is $T$,then the time taken to cover the first half length is:

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The linear mass density of a vibrating string is $1.3 \times 10^{-4} \ kg/m$. $A$ transverse wave is propagating on the string and is described by the equation $y = 0.021 \sin(x + 30t)$,where $x$ and $y$ are measured in meters and $t$ in seconds. The tension in the string is approximately: (in $N$)

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$A$ transverse wave is passing through a string as shown in the figure. The mass density of the string is $1 \ kg/m^3$ and the cross-sectional area of the string is $0.01 \ m^2$. The equation of the wave in the string is $y = 2 \sin(20t - 10x)$. The hanging mass is (in $kg$):-

$A$ transverse wave propagating on a stretched string of linear density $3 \times 10^{-4} \ kg \ m^{-1}$ is represented by the equation $y = 0.2 \sin (1.5 x + 60 t)$, where $x$ is in metres and $t$ is in seconds. The tension in the string (in newton) is

$A$ rope of length $L$ and mass $M$ hangs freely from the ceiling. If the time taken by a transverse wave to travel from the bottom to the top of the rope is $T$,then the time taken to cover the first half length is:

The linear mass density of a vibrating string is $1.3 \times 10^{-4} \ kg/m$. $A$ transverse wave is propagating on the string and is described by the equation $y = 0.021 \sin(x + 30t)$,where $x$ and $y$ are measured in meters and $t$ in seconds. The tension in the string is approximately: (in $N$)

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